533 – Modeling Confounders via Smoothing and Regularization Methods? The Case of Age-Period-Cohort and Beyond
Solving the Identifiability Problem with the Lasso Regularization in Age-Period-Cohort Analysis
Beverly Fu
Okemos High School
Statistical age-period-cohort analysis has been studied extensively in the literature and has many applications to demography, public health, and sociology. However, due to the linear dependence of age, period and cohort, the regression model suffers from the identifiability problem, where multiple estimators fit the model equally well, making it difficult to determine which estimator yields the correct parameter estimation. In this work, I apply the Lasso shrinkage method, which not only helps to determine a unique estimate, but also yields consistent feature selection since the Lasso estimator yields consistent variable selection if the covariates of the model satisfy the irrepresentable condition. We apply the Lasso to the eigenvectors of the design matrix and thus the irrepresentable condition is satisfied as it sets the coefficient for the null eigenvector to 0, leading to consistent estimation. We will compare the Lasso estimator with the intrinsic estimator in real data examples and illustrate that the Lasso method works well and yields sensible trend estimation in age, period and cohort.